There were some oranges and persimmons in Container W and Container X. In Container W, the ratio of the oranges to the number of persimmons was 3 : 1. In Container X, the ratio of the number of oranges to the number of persimmons was 3 : 1. There were 3 times as many fruits in Container W as in Container X. After another 64 persimmons were put into Container X, the ratio of the number of oranges to the number of persimmons in Container X became 1 : 3. How many fruits were there in Container W?

Container W		Container X
3x4 = 12 u		1x4 = 4 u
Oranges	Persimmons	Oranges	Persimmons
3x3	1x3	3	1
9 u	3 u	3 u	1 u

The total number of fruits in Container W is repeated.  Make the total number of fruits in Container W the same.  LCM of 3 and 4 is 12.

The total number of fruits in Container X at first is repeated.  Make the total number of fruits in Container X the same.  LCM of 1 and 4 is 4.

	Container W		Container X
	Oranges	Persimmons	Oranges	Persimmons
Before	9 u	3 u	3 u	1 u
Change				+ 64
After	9 u	3 u	1x3 = 3 u	3x3 = 9 u

Number of oranges in Container X remains unchanged.  Make the number of oranges in Container X the same.  LCM of 3 and 1 is 3.

Number of persimmons put into Container X
= 9 u - 1 u
= 8 u

8 u = 64

1 u = 64 ÷ 8 = 8

Number of fruits in Container W
= 9 u + 3 u
= 12 u
= 12 x 8
= 96

Answer(s): 96